(* Copyright (C) 2004, HELM Team. * * This file is part of HELM, an Hypertextual, Electronic * Library of Mathematics, developed at the Computer Science * Department, University of Bologna, Italy. * * HELM is free software; you can redistribute it and/or * modify it under the terms of the GNU General Public License * as published by the Free Software Foundation; either version 2 * of the License, or (at your option) any later version. * * HELM is distributed in the hope that it will be useful, * but WITHOUT ANY WARRANTY; without even the implied warranty of * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the * GNU General Public License for more details. * * You should have received a copy of the GNU General Public License * along with HELM; if not, write to the Free Software * Foundation, Inc., 59 Temple Place - Suite 330, Boston, * MA 02111-1307, USA. * * For details, see the HELM World-Wide-Web page, * http://helm.cs.unibo.it/ *) open Printf module Constr = MetadataConstraints module PET = ProofEngineTypes exception Goal_is_not_an_equation let debug = false let debug_print s = if debug then prerr_endline (Lazy.force s) (** maps a shell like pattern (which uses '*' and '?') to a sql pattern for * the "like" operator (which uses '%' and '_'). Does not support escaping. *) let sqlpat_of_shellglob = let star_RE, qmark_RE, percent_RE, uscore_RE = Pcre.regexp "\\*", Pcre.regexp "\\?", Pcre.regexp "%", Pcre.regexp "_" in fun shellglob -> Pcre.replace ~rex:star_RE ~templ:"%" (Pcre.replace ~rex:qmark_RE ~templ:"_" (Pcre.replace ~rex:percent_RE ~templ:"\\%" (Pcre.replace ~rex:uscore_RE ~templ:"\\_" shellglob))) let nonvar uri = not (UriManager.uri_is_var uri) let locate ~(dbd:HMysql.dbd) ?(vars = false) pat = let sql_pat = sqlpat_of_shellglob pat in let query = sprintf ("SELECT source FROM %s WHERE value LIKE \"%s\" UNION "^^ "SELECT source FROM %s WHERE value LIKE \"%s\"") (MetadataTypes.name_tbl ()) sql_pat MetadataTypes.library_name_tbl sql_pat in let result = HMysql.exec dbd query in List.filter nonvar (HMysql.map result (fun cols -> match cols.(0) with Some s -> UriManager.uri_of_string s | _ -> assert false)) let match_term ~(dbd:HMysql.dbd) ty = (* debug_print (lazy (CicPp.ppterm ty)); *) let metadata = MetadataExtractor.compute ~body:None ~ty in let constants_no = MetadataConstraints.UriManagerSet.cardinal (MetadataConstraints.constants_of ty) in let full_card, diff = if CicUtil.is_meta_closed ty then Some (MetadataConstraints.Eq constants_no), None else let diff_no = let (hyp_constants, concl_constants) = (* collect different constants in hypotheses and conclusions *) List.fold_left (fun ((hyp, concl) as acc) metadata -> match (metadata: MetadataTypes.metadata) with | `Sort _ | `Rel _ -> acc | `Obj (uri, `InConclusion) | `Obj (uri, `MainConclusion _) when not (List.mem uri concl) -> (hyp, uri :: concl) | `Obj (uri, `InHypothesis) | `Obj (uri, `MainHypothesis _) when not (List.mem uri hyp) -> (uri :: hyp, concl) | `Obj _ -> acc) ([], []) metadata in List.length hyp_constants - List.length concl_constants in let (concl_metas, hyp_metas) = MetadataExtractor.compute_metas ty in let diff = if MetadataExtractor.IntSet.equal concl_metas hyp_metas then Some (MetadataConstraints.Eq diff_no) else if MetadataExtractor.IntSet.subset concl_metas hyp_metas then Some (MetadataConstraints.Gt (diff_no - 1)) else if MetadataExtractor.IntSet.subset hyp_metas concl_metas then Some (MetadataConstraints.Lt (diff_no + 1)) else None in None, diff in let constraints = List.map MetadataTypes.constr_of_metadata metadata in Constr.at_least ~dbd ?full_card ?diff constraints let ( ** ) x y = int_of_float ((float_of_int x) ** (float_of_int y)) let signature_of_hypothesis context = List.fold_left (fun set hyp -> match hyp with | None -> set | Some (_, Cic.Decl t) | Some (_, Cic.Def (t, _)) -> Constr.UriManagerSet.union set (Constr.constants_of t)) Constr.UriManagerSet.empty context let intersect uris siguris = let set1 = List.fold_right Constr.UriManagerSet.add uris Constr.UriManagerSet.empty in let set2 = List.fold_right Constr.UriManagerSet.add siguris Constr.UriManagerSet.empty in let inter = Constr.UriManagerSet.inter set1 set2 in List.filter (fun s -> Constr.UriManagerSet.mem s inter) uris (* Profiling code let at_most = let profiler = CicUtil.profile "at_most" in fun ~dbd ~where uri -> profiler.profile (Constr.at_most ~dbd ~where) uri let sigmatch = let profiler = CicUtil.profile "sigmatch" in fun ~dbd ~facts ~where signature -> profiler.profile (MetadataConstraints.sigmatch ~dbd ~facts ~where) signature *) let at_most = Constr.at_most let sigmatch = MetadataConstraints.sigmatch let filter_uris_forward ~dbd (main, constants) uris = let main_uris = match main with | None -> [] | Some (main, types) -> main :: types in let full_signature = List.fold_right Constr.UriManagerSet.add main_uris constants in List.filter (at_most ~dbd ~where:`Statement full_signature) uris let filter_uris_backward ~dbd ~facts signature uris = let siguris = List.map snd (sigmatch ~dbd ~facts ~where:`Statement signature) in intersect uris siguris let compare_goal_list proof goal1 goal2 = let _,metasenv,_,_ = proof in let (_, ey1, ty1) = CicUtil.lookup_meta goal1 metasenv in let (_, ey2, ty2) = CicUtil.lookup_meta goal2 metasenv in let ty_sort1,_ = CicTypeChecker.type_of_aux' metasenv ey1 ty1 CicUniv.empty_ugraph in let ty_sort2,_ = CicTypeChecker.type_of_aux' metasenv ey2 ty2 CicUniv.empty_ugraph in let prop1 = let b,_ = CicReduction.are_convertible ey1 (Cic.Sort Cic.Prop) ty_sort1 CicUniv.empty_ugraph in if b then 0 else 1 in let prop2 = let b,_ = CicReduction.are_convertible ey2 (Cic.Sort Cic.Prop) ty_sort2 CicUniv.empty_ugraph in if b then 0 else 1 in prop1 - prop2 (* experimental_hint is a version of hint for experimental purposes. It uses auto_tac_verbose instead of auto tac. Auto_tac verbose also returns a substitution - for the moment as a function from cic to cic, to be changed into an association list in the future -. This substitution is used to build a hash table of the inspected goals with their associated proofs. The cose is a cut and paste of the previous one: at the end of the experimentation we shall make a choice. *) let close_with_types s metasenv context = Constr.UriManagerSet.fold (fun e bag -> let t = CicUtil.term_of_uri e in let ty, _ = CicTypeChecker.type_of_aux' metasenv context t CicUniv.empty_ugraph in Constr.UriManagerSet.union bag (Constr.constants_of ty)) s s let close_with_constructors s metasenv context = Constr.UriManagerSet.fold (fun e bag -> let t = CicUtil.term_of_uri e in match t with Cic.MutInd (uri,_,_) | Cic.MutConstruct (uri,_,_,_) -> (match fst (CicEnvironment.get_obj CicUniv.empty_ugraph uri) with Cic.InductiveDefinition(tl,_,_,_) -> snd (List.fold_left (fun (i,s) (_,_,_,cl) -> let _,s = List.fold_left (fun (j,s) _ -> let curi = UriManager.uri_of_uriref uri i (Some j) in j+1,Constr.UriManagerSet.add curi s) (1,s) cl in (i+1,s)) (0,bag) tl) | _ -> assert false) | _ -> bag) s s (* Profiling code let apply_tac_verbose = let profiler = CicUtil.profile "apply_tac_verbose" in fun ~term status -> profiler.profile (PrimitiveTactics.apply_tac_verbose ~term) status let sigmatch = let profiler = CicUtil.profile "sigmatch" in fun ~dbd ~facts ?(where=`Conclusion) signature -> profiler.profile (Constr.sigmatch ~dbd ~facts ~where) signature let cmatch' = let profiler = CicUtil.profile "cmatch'" in fun ~dbd ~facts signature -> profiler.profile (Constr.cmatch' ~dbd ~facts) signature *) let apply_tac_verbose = PrimitiveTactics.apply_tac_verbose let cmatch' = Constr.cmatch' let signature_of_goal ~(dbd:HMysql.dbd) ((proof, goal) as status) = let (_, metasenv, _, _) = proof in let (_, context, ty) = CicUtil.lookup_meta goal metasenv in let main, sig_constants = Constr.signature_of ty in let set = signature_of_hypothesis context in let set = match main with None -> set | Some (main,l) -> List.fold_right Constr.UriManagerSet.add (main::l) set in let set = Constr.UriManagerSet.union set sig_constants in let all_constants_closed = close_with_types set metasenv context in let uris = sigmatch ~dbd ~facts:false ~where:`Statement (None,all_constants_closed) in let uris = List.filter nonvar (List.map snd uris) in let uris = List.filter Hashtbl_equiv.not_a_duplicate uris in uris let equations_for_goal ~(dbd:HMysql.dbd) ((proof, goal) as status) = let to_string set = "{ " ^ (String.concat ", " (Constr.UriManagerSet.fold (fun u l -> (UriManager.string_of_uri u)::l) set [])) ^ " }" in let (_, metasenv, _, _) = proof in let (_, context, ty) = CicUtil.lookup_meta goal metasenv in let main, sig_constants = Constr.signature_of ty in (* Printf.printf "\nsig_constants: %s\n\n" (to_string sig_constants); *) (* match main with *) (* None -> raise Goal_is_not_an_equation *) (* | Some (m,l) -> *) let m, l = let eq_URI = let us = UriManager.string_of_uri (LibraryObjects.eq_URI ()) in UriManager.uri_of_string (us ^ "#xpointer(1/1)") in match main with | None -> eq_URI, [] | Some (m, l) when UriManager.eq m eq_URI -> m, l | Some (m, l) -> eq_URI, [] in Printf.printf "\nSome (m, l): %s, [%s]\n\n" (UriManager.string_of_uri m) (String.concat "; " (List.map UriManager.string_of_uri l)); (* if m == UriManager.uri_of_string HelmLibraryObjects.Logic.eq_XURI then ( *) let set = signature_of_hypothesis context in (* Printf.printf "\nsignature_of_hypothesis: %s\n\n" (to_string set); *) let set = Constr.UriManagerSet.union set sig_constants in let set = close_with_types set metasenv context in (* Printf.printf "\ndopo close_with_types: %s\n\n" (to_string set); *) let set = close_with_constructors set metasenv context in (* Printf.printf "\ndopo close_with_constructors: %s\n\n" (to_string set); *) let set = List.fold_right Constr.UriManagerSet.remove (m::l) set in let uris = sigmatch ~dbd ~facts:false ~where:`Statement (main,set) in let uris = List.filter nonvar (List.map snd uris) in let uris = List.filter Hashtbl_equiv.not_a_duplicate uris in uris (* ) *) (* else raise Goal_is_not_an_equation *) let experimental_hint ~(dbd:HMysql.dbd) ?(facts=false) ?signature ((proof, goal) as status) = let (_, metasenv, _, _) = proof in let (_, context, ty) = CicUtil.lookup_meta goal metasenv in let (uris, (main, sig_constants)) = match signature with | Some signature -> (sigmatch ~dbd ~facts signature, signature) | None -> (cmatch' ~dbd ~facts ty, Constr.signature_of ty) in let uris = List.filter nonvar (List.map snd uris) in let uris = List.filter Hashtbl_equiv.not_a_duplicate uris in let types_constants = match main with | None -> Constr.UriManagerSet.empty | Some (main, types) -> List.fold_right Constr.UriManagerSet.add (main :: types) Constr.UriManagerSet.empty in let all_constants = let hyp_and_sug = Constr.UriManagerSet.union (signature_of_hypothesis context) sig_constants in let main = match main with | None -> Constr.UriManagerSet.empty | Some (main,_) -> let ty, _ = CicTypeChecker.type_of_aux' metasenv context (CicUtil.term_of_uri main) CicUniv.empty_ugraph in Constr.constants_of ty in Constr.UriManagerSet.union main hyp_and_sug in (* Constr.UriManagerSet.iter debug_print hyp_constants; *) let all_constants_closed = close_with_types all_constants metasenv context in let other_constants = Constr.UriManagerSet.diff all_constants_closed types_constants in debug_print (lazy "all_constants_closed"); if debug then Constr.UriManagerSet.iter (fun s -> debug_print (lazy (UriManager.string_of_uri s))) all_constants_closed; debug_print (lazy "other_constants"); if debug then Constr.UriManagerSet.iter (fun s -> debug_print (lazy (UriManager.string_of_uri s))) other_constants; let uris = let pow = 2 ** (Constr.UriManagerSet.cardinal other_constants) in if ((List.length uris < pow) or (pow <= 0)) then begin debug_print (lazy "MetadataQuery: large sig, falling back to old method"); filter_uris_forward ~dbd (main, other_constants) uris end else filter_uris_backward ~dbd ~facts (main, other_constants) uris in let rec aux = function | [] -> [] | uri :: tl -> (let status' = try let (subst,(proof, goal_list)) = (* debug_print (lazy ("STO APPLICANDO" ^ uri)); *) apply_tac_verbose ~term:(CicUtil.term_of_uri uri) status in let goal_list = List.stable_sort (compare_goal_list proof) goal_list in Some (uri, (subst,(proof, goal_list))) with ProofEngineTypes.Fail _ -> None in match status' with | None -> aux tl | Some status' -> status' :: aux tl) in List.stable_sort (fun (_,(_, (_, goals1))) (_,(_, (_, goals2))) -> Pervasives.compare (List.length goals1) (List.length goals2)) (aux uris) let new_experimental_hint ~(dbd:HMysql.dbd) ?(facts=false) ?signature ~universe ((proof, goal) as status) = let (_, metasenv, _, _) = proof in let (_, context, ty) = CicUtil.lookup_meta goal metasenv in let (uris, (main, sig_constants)) = match signature with | Some signature -> (sigmatch ~dbd ~facts signature, signature) | None -> (cmatch' ~dbd ~facts ty, Constr.signature_of ty) in let universe = List.fold_left (fun res u -> Constr.UriManagerSet.add u res) Constr.UriManagerSet.empty universe in let uris = List.fold_left (fun res (_,u) -> Constr.UriManagerSet.add u res) Constr.UriManagerSet.empty uris in let uris = Constr.UriManagerSet.inter uris universe in let uris = Constr.UriManagerSet.elements uris in let rec aux = function | [] -> [] | uri :: tl -> (let status' = try let (subst,(proof, goal_list)) = (* debug_print (lazy ("STO APPLICANDO" ^ uri)); *) apply_tac_verbose ~term:(CicUtil.term_of_uri uri) status in let goal_list = List.stable_sort (compare_goal_list proof) goal_list in Some (uri, (subst,(proof, goal_list))) with ProofEngineTypes.Fail _ -> None in match status' with | None -> aux tl | Some status' -> status' :: aux tl) in List.stable_sort (fun (_,(_, (_, goals1))) (_,(_, (_, goals2))) -> Pervasives.compare (List.length goals1) (List.length goals2)) (aux uris) let elim ~dbd uri = let constraints = [`Rel [`MainConclusion None]; `Sort (Cic.Prop,[`MainHypothesis (Some (MetadataTypes.Ge 1))]); `Obj (uri,[`MainHypothesis (Some (MetadataTypes.Eq 0))]); `Obj (uri,[`InHypothesis]); ] in MetadataConstraints.at_least ~rating:`Hits ~dbd constraints let fill_with_dummy_constants t = let rec aux i types = function Cic.Lambda (n,s,t) -> let dummy_uri = UriManager.uri_of_string ("cic:/dummy_"^(string_of_int i)^".con") in (aux (i+1) (s::types) (CicSubstitution.subst (Cic.Const(dummy_uri,[])) t)) | t -> t,types in let t,types = aux 0 [] t in t, List.rev types let instance ~dbd t = let t',types = fill_with_dummy_constants t in let metadata = MetadataExtractor.compute ~body:None ~ty:t' in (* List.iter (fun x -> debug_print (lazy (MetadataPp.pp_constr (MetadataTypes.constr_of_metadata x)))) metadata; *) let no_concl = MetadataDb.count_distinct `Conclusion metadata in let no_hyp = MetadataDb.count_distinct `Hypothesis metadata in let no_full = MetadataDb.count_distinct `Statement metadata in let is_dummy = function | `Obj(s, _) -> (String.sub (UriManager.string_of_uri s) 0 10) <> "cic:/dummy" | _ -> true in let rec look_for_dummy_main = function | [] -> None | `Obj(s,`MainConclusion (Some (MetadataTypes.Eq d)))::_ when (String.sub (UriManager.string_of_uri s) 0 10 = "cic:/dummy") -> let s = UriManager.string_of_uri s in let len = String.length s in let dummy_index = int_of_string (String.sub s 11 (len-15)) in let dummy_type = List.nth types dummy_index in Some (d,dummy_type) | _::l -> look_for_dummy_main l in match (look_for_dummy_main metadata) with | None-> (* debug_print (lazy "Caso None"); *) (* no dummy in main position *) let metadata = List.filter is_dummy metadata in let constraints = List.map MetadataTypes.constr_of_metadata metadata in let concl_card = Some (MetadataConstraints.Eq no_concl) in let full_card = Some (MetadataConstraints.Eq no_full) in let diff = Some (MetadataConstraints.Eq (no_hyp - no_concl)) in Constr.at_least ~dbd ?concl_card ?full_card ?diff constraints | Some (depth, dummy_type) -> (* debug_print (lazy (sprintf "Caso Some %d %s" depth (CicPp.ppterm dummy_type))); *) (* a dummy in main position *) let metadata_for_dummy_type = MetadataExtractor.compute ~body:None ~ty:dummy_type in (* Let us skip this for the moment let main_of_dummy_type = look_for_dummy_main metadata_for_dummy_type in *) let metadata = List.filter is_dummy metadata in let constraints = List.map MetadataTypes.constr_of_metadata metadata in let metadata_for_dummy_type = List.filter is_dummy metadata_for_dummy_type in let metadata_for_dummy_type, depth' = (* depth' = the depth of the A -> A -> Prop *) List.fold_left (fun (acc,dep) c -> match c with | `Sort (s,`MainConclusion (Some (MetadataTypes.Eq i))) -> (`Sort (s,`MainConclusion (Some (MetadataTypes.Ge i))))::acc, i | `Obj (s,`MainConclusion (Some (MetadataTypes.Eq i))) -> (`Obj (s,`MainConclusion (Some (MetadataTypes.Ge i))))::acc, i | `Rel (`MainConclusion (Some (MetadataTypes.Eq i))) -> (`Rel (`MainConclusion (Some (MetadataTypes.Ge i))))::acc, i | _ -> (c::acc,dep)) ([],0) metadata_for_dummy_type in let constraints_for_dummy_type = List.map MetadataTypes.constr_of_metadata metadata_for_dummy_type in (* start with the dummy constant in main conlusion *) let from = ["refObj as table0"] in let where = [sprintf "table0.h_position = \"%s\"" MetadataTypes.mainconcl_pos; sprintf "table0.h_depth >= %d" depth] in let (n,from,where) = List.fold_left (MetadataConstraints.add_constraint ~start:2) (2,from,where) constraints in let concl_card = Some (MetadataConstraints.Eq no_concl) in let full_card = Some (MetadataConstraints.Eq no_full) in let diff = Some (MetadataConstraints.Eq (no_hyp - no_concl)) in let (n,from,where) = MetadataConstraints.add_all_constr (n,from,where) concl_card full_card diff in (* join with the constraints over the type of the constant *) let where = (sprintf "table0.h_occurrence = table%d.source" n)::where in let where = sprintf "table0.h_depth - table%d.h_depth = %d" n (depth - depth')::where in let (m,from,where) = List.fold_left (MetadataConstraints.add_constraint ~start:n) (n,from,where) constraints_for_dummy_type in Constr.exec ~dbd (m,from,where) (* fwd_simpl ****************************************************************) let rec map_filter f n = function | [] -> [] | hd :: tl -> match f n hd with | None -> map_filter f (succ n) tl | Some hd -> hd :: map_filter f (succ n) tl let get_uri t = let aux = function | Cic.Appl (hd :: tl) -> Some (CicUtil.uri_of_term hd, tl) | hd -> Some (CicUtil.uri_of_term hd, []) in try aux t with | Invalid_argument "uri_of_term" -> None let get_metadata t = let f n t = match get_uri t with | None -> None | Some (uri, _) -> Some (n, uri) in match get_uri t with | None -> None | Some (uri, args) -> Some (uri, map_filter f 1 args) let debug_metadata = function | None -> () | Some (outer, inners) -> let f (n, uri) = Printf.eprintf "%s: %i %s\n" "fwd" n (UriManager.string_of_uri uri) in Printf.eprintf "\n%s: %s\n" "fwd" (UriManager.string_of_uri outer); List.iter f inners; prerr_newline () let fwd_simpl ~dbd t = let map inners row = match row.(0), row.(1), row.(2) with | Some source, Some inner, Some index -> source, List.mem (int_of_string index, (UriManager.uri_of_string inner)) inners | _ -> "", false in let rec rank ranks (source, ok) = match ranks, ok with | [], false -> [source, 0] | [], true -> [source, 1] | (uri, i) :: tl, false when uri = source -> (uri, 0) :: tl | (uri, 0) :: tl, true when uri = source -> (uri, 0) :: tl | (uri, i) :: tl, true when uri = source -> (uri, succ i) :: tl | hd :: tl, _ -> hd :: rank tl (source, ok) in let compare (_, x) (_, y) = compare x y in let filter n (uri, rank) = if rank > 0 then Some (UriManager.uri_of_string uri) else None in let metadata = get_metadata t in debug_metadata metadata; match metadata with | None -> [] | Some (outer, inners) -> let select = "source, h_inner, h_index" in let from = "genLemma" in let where = Printf.sprintf "h_outer = \"%s\"" (HMysql.escape (UriManager.string_of_uri outer)) in let query = Printf.sprintf "SELECT %s FROM %s WHERE %s" select from where in let result = HMysql.exec dbd query in let lemmas = HMysql.map ~f:(map inners) result in let ranked = List.fold_left rank [] lemmas in let ordered = List.rev (List.fast_sort compare ranked) in map_filter filter 0 ordered (* get_decomposables ********************************************************) let decomposables ~dbd = let map row = match row.(0) with | None -> None | Some str -> match CicUtil.term_of_uri (UriManager.uri_of_string str) with | Cic.MutInd (uri, typeno, _) -> Some (uri, typeno) | _ -> raise (UriManager.IllFormedUri str) in let select, from = "source", "decomposables" in let query = Printf.sprintf "SELECT %s FROM %s" select from in let decomposables = HMysql.map ~f:map (HMysql.exec dbd query) in map_filter (fun _ x -> x) 0 decomposables